Question

A regular pentagon with a perimeter of 10 cm is dilated by a scale factor of 3/2 to create a new pentagon. What is the the perimeter of the new pentagon?

Answer 1

Given:

Perimeter of a regular pentagon = 10 cm

The pentagon is dilated by a scale factor =
`(3)/(2)`.

To find:

The perimeter of the new pentagon.

Solution:

If a figure is dilated by a scale factor k, then

Perimeter of new figure = k × perimeter of original figure

The scale factor is
`(3)/(2)` and the perimeter of a regular pentagon is 10 cm. So, the perimeter of a new pentagon is:

`\text{Perimeter of new pentagon}=(3)/(2)* 10`

`\text{Perimeter of new pentagon}=3* 5`

`\text{Perimeter of new pentagon}=15`

Therefore, the perimeter of the new pentagon is 15 cm.